I have an old but adequate jig/sabre saw that I don't seem to be able to find blades for. I know there are T-shank and U-shank blades and my saw seems to use the latter but the blades I've been able to find recently have a shank so narrow that after a few inches of cutting, the blade angles back so that the tip trails the part fixed in the saw. It seems I need a wider shank but I can't find them. Or any kind of useful comparison between types of blades for this type of saw.

The saw is a cheap, old, no-name tool but it works it it would be nice if I could get blades for my occasional use.

A picture of where the blade is attached would be helpful. Some sabre saws have a collar that goes over the reciprocating shaft. If that were missing it could cause the symptom you describe.
– scannyDec 27 '16 at 0:32

Looking at your picture, I'm struck by the realization that the cup or U at the top should slide up against the pin visible to the left of the screw in my picture and the screw should set into the hole. My old blades have the hole, the new ones do not. That's what I need to look for. Thank you!
– Chris NelsonDec 28 '16 at 0:42